Position plotter for hyperbolic radio survey system



Fel 26, 1952 JL E. HAwKlNs E-rAL 2,587,467

POSITION PLOTTER FOR HYPERBOLIC RADIO SURVEY SYSTEM Filed July 19, 19494 Sheets-Sheet l Feb- 25, 1952 J. E. HAwKlNs ETAL 2,587,467

POSITION PLOTTER FOR HYPERBOLIC RADIO SURVEY SYSTEM 4 Sheets-Sheet 2Filed July 19. 1949 y IN VEN TORS. James 6. Walz/kms BY Robert I0.alzasser J. E. HAWKINS EVAL Feb. 26, 1952 POSITION PLOTTER FORHYPERBOLIC RADIO SRVEY SYSTEM 4 Sheets-Sheet 3 Filed July 19, 1949 INVEN TORS. Haw/(m5 Robert ZD.' ctliosser BY Feb. 26, 1952 J. E. HAwKlNsErm. 2,587,457

POSITION PLOTTER FOR HYPERBOLIC RADIO SURVEY SYSTEM Filed July 19, 19494 Sheets-Sheet 4 IN VEN TORS. James Wzwkzzs Y Roberf ZU. aif ser atenteFe, 26, 1952 2,587,467 POSITION PLOTTER FOR HYPERBOLIC RADIO SURVEYSYSTEM James E. Hawkins and Robert W.

Baltosser,

Tulsa, Okla., assiznors to Seismograph Service Corporation, Tulsa, OklaDelaware a corporation of Application July 19, 1949, Serial No. 105,582

I'he present invention relates to position computing and plottingapparatus and more particularly to improvements in signal receiving andposition computing apparatus for use in radio positionV finding systemsof the hyperbolic continuous wave type employing phase comparison inpairs of position indication signals radiated from at least three spacedtransmitting points to provide indications or measures from which theposition of a mobile receiving point relative to the known positions ofthe transmitting points are mechanically and automatically computed soas to provide a continuous position indication on a chart or the like.

In systems of the particular type referred to,

the continuous waves radiated from each pair.

of transmitters produce standing waves in space, the phase relationshipof which changes as a function of changing position between the twotransmitting points. More specifically, the standing waves produced byeach pair of transmitting unitsof the system are characterized byisophase lines which are hyperbolic in contour about the transmittingpoints as foci. On aline bisecting the pair of transmitters. theseiso-phase lines are spaced apart a distance equal to one-half the meanwavelength of the radiated waves and have diverging spacings at pointson either side of this line. With this system arrangement, the positionof a receiving point relative to a pair of hyperbolic iso-phase linesmay be determined by measuring the phase relationship between continuouswaves radiated from the pair of transmitters. Since the point oflocation of the receiving point along the zone separating the twoiso-phase lines is not indicated by such a phase measurement, it becomesnecessary to employ at least three spaced transmitters, different pairsof which function to provide a grid-like pattern of intersectinghyperbolic lines, in order to obtain. absolute determination of theposition of the receiving point.

In systems of the continuous wave hyperbolic typeheretofore proposedpairs of phase comparison means including indicator members 4have beenemployed to provide two visual indications which respectively reflectthe position of the receiyin'gk, point relative to the two setsof-hyperbolicdao-phase lines, and the geographic position of thereceiving point relative to the known positions of the transmitters maybe manually located on specially prepared hyperbolic gridtype charts ormaps. Such operations, however, are time consuming and require accuratecounting by the observer or operator of the iso-phase lines or lanes onthe chart in order to insure proper determination of the map position ofthe receiving apparatus. Moreover the preparation of the grid-typecharts requires the exercise of great care and accuracy, and it isaccordingly an object of the present invention to provide a mechanicalcomputing apparatus which is capable either of accurately plotting ahyperbolic grid or chart consisting of two families of hyperbolic curveshaving one common focal point or of accurately tracing or continuouslyindicating on a map or chart (either with or without a hyperbolic gridpattern) the position of the receiving apparatus as reflected by themovement of the movable members of the phase comparison means.

It is another object of the invention to provide improved mechanicalcomputing and plotting apparatus for generating hyperbolic curves of atleast two intersecting families to form a hyperbolic intersection grid.

It is still another object of the invention to provide improvedreceiving and mechanical position computing or tracing apparatus whichis uniquely adapted for -use in position determining systems of thecharacter described.

It is a further object of the invention to provide improved radioposition nding systems of the hyperbolic continuous wave typeincorporating receiving apparatus including computing and tracingmechanism capable of continuously indicating the position of thereceiving apparatus relative to a plurality of known positions whichconstitute the focal points of a hyperbolic intersection grid.

Receiving and position computing and tracing apparatus embodying thepresent invention is highly useful in various types of radio positionfinding systems such, for example, as systenis of the type disclosed inthe Honore Patent No. 2,148,617 in which the carrier waves of each pairof transmitters are heterodyned at a iixed link transmitting point, andthe difference frequency components of the heterodyned waves aremodulated as reference signals upon the carrier output of the linktransmitter or transmitters for radiation to the receiving point, wherethe difference frequency components a're detected and respectively phasecompared with the corresponding difference frequency signals derived bydirectly heterodyning the corresponding pairs of transmitted continuouswaves at the receiving point. Moreover, apparatus embodying theinvention is particularly applicable to and is herein described asembodied ai modified form of positio l Fis; 'gi' is; a: Idaan view Il??@ed in thgapparatu Fgg s ripper ma finer ,embodiment :of: @th

n l {Referringnowrothe drawin cularly to Figs@ 1; to 5, inclusive; the present yinv Patent No. 2,551,211 granted May 1, 1951 in the jects andadvantages thereof, will best be under- .I

stood by reference to the specification taken in connection with theaccompanying drawings, in which:

Fig. 1 is a diagrammatic illustration of an improved radio positiondetermining system including receiving and position computing or tracingapparatus embodying the present invention;

Fig. 2 is an elevational view on a somewhat larger scale of a portion ofthe computing and tracing apparatus shown in Fig. 1;

Fig. 3 is a plan view of the computing and tracing apparatus shown inFigs. 1 and 2;

Fig. 4 is an enlarged detail View of the tracing element employed in theposition computing and tracing apparatus;

Fig. 5 is a diagrammatic view showing an intersecting hyperbolic gridwhich may be produced by or which may be employed with the computing andtracing apparatus;

Fig. 6 is a plan view similar to Fig. 3 showing where.

fru `aiterna;tcly rendering theseltwo transmitters opf-y er toillust-ratethe action whichA aan is i illustrated; .as ems() ma i in; agsystem vrovidin'g position: information at la mobile ngc-r- 1,

inse uns 13; :whim may 'r vehicle opera-limsi Wlh ft igszinar" wa e.

eiesg together with? switching miam flr erative. In ord occurs, arrowpointed solid lines have been shown in Fig. 1 of the drawings toindicate the receiving points of signal acceptance and the sources ofthe accepted signals during each 4period when the transmitter 20 isoperating, and arrow pointed dashed lines have been shown to illustratethe receiving points of signal acceptance a'nd the Sources of acceptedsignals during each period when the transmitter 2| is operating. From aconsideration of these lines and reflection upon the above explanation,it will be understood that the receivers 26 and 21 (to be more fullydescribed hereinafter) alternately function as reference signaldetecting receivers and as heterodyning receivers for developing therequired heterodyne or difference frequency signals. In the arrangementillustrated, keying of the two transmitters 20 and 2| for alternateoperation is accomplished by alternately feeding anode current to theelectron discharge tubes of the respective transmitters from thepositive terminal 25 of the anode current source, not shown, through acommutating ring 22 which is shaft connected by means of a shaft 24 tobe driven at a constant speed by a synchronous motor and gear train unit23. More specifically. the positive terminal 25 of the anode currentsource is connected to the conductive segment 22h of the commutatingring 22, which segment spans slightly less than half the circumferenceof the ring. The remainder of the ring is comprised of an insulatingsegment 22a. At diametrically opposed points around the circumference ofthe ring, brushes 22o and 22d are provided which engage the ringperiphery. These brushes are respectively connected to the positive busconductors ofthe two transmitters 20 and 2 I, such that anode current isalternately delivered to the electron discharge tubes of the twotransmitters. Since the conductive segment 22b of the ring 22 representsslightly less than half the periphery surface of the ring, it will beunderstood that a short off-signal period is provided between successiveperiods during which the transmitters 20 and 2| are alternatelyoperated, thus preventing simultaneous radiation of waves by bothtransmitters. The periodicity with which the two transmitters 20 and 2|are alternately operated is, of course, dependent upon the speed ofrotation of thecommutating ring 22. Preferably, this ring is driven at aspeed of one revolution per second such that transmitters 20 and 2| areeach rendered operative at one-half second intervals.

As indicated above, the carrier frequencies at which the fourtransmitters of the three transmitting units I0, II and I2 operate areall different.l

Preferably, however, these carrier waves are so paired that thefrequencies of each pair are well within a single channel allocation ofkilocycles as specified by the Federal Communications Commission of theUnited States Government. To this end, the output frequency of thetransmitter and the output frequency of the transmitter in the unit I2,forming the first transmitter pair, may be 1601.875 and 1602.125kilocycles respectively, such that the difference frequency therebetweenis 0.250 kilocycle, while the output frequencies of the transmitter 2|and the transmitter of the unit I0, forming the second transmitter pair,may be 1699.700 and 1700.300 kilocycles, respectively, such that thedifference frequency therebetween is 0.600 kilocycle. It will be notedthat the channels in which the two pairs of carrier frequencies fall areseparated in the frequency spectrum by approximately l100 kilocycles,thus facilitating selective reception of these carrier pairs in themanner more fully explained below. The power of the four transmitters issuch that the entire area in which position information mayl be desiredaboard the vehicle or vessel carrying the receiving unit I3 is blanketedwith waves radiated from each of the four transmitters and that thesewaves have a eld strength at all points within this area suicient topermit reliable reception without requiring undue sensitivity of the l vreceiving equipment.

The transmitting units I0 and I2 are respec-i tively provided with meansfor alternatelymodulating the waves radiated by the transmitters of theunits I0 and I2 with reference signals representative of the differencefrequencies between the carrier wave pairs. may be received at anyreceiving point, such, for example, as at the mobile receiving unit I3,located within the radius of transmission of the four transmitters.'I'he equipment for this purpose as provided at the transmitting unit I0comprises a fixed tuned amplitude modulation receiver I6, center tunedto a frequency of 1602 kilocycles and sharply selective to the 1601.875and'1602.125 kilocycle carrier waves respectively radiated by thetransmitter 20 and the transmitter of the unit I2. The selectivity ofthis receiver is obviously such that the carrier waves radiated by thetransmitter 2| and the transmitter of the unit I0 are rejected in theradio frequency section thereof. The beat frequency of 0.250 kilocyclebetween the two carriers accepted by the radio frequencysection of thereceiver i6 is reproduced in the audio frequency section of thisreceiver and These reference signals delivered to the modulator I5, foramplitude modulation upon the carrier output of the transmitter embodiedin the unit II), through a narrow band pass filter 8, which is centertuned to a fre-l e. quency of 0.250 kiiocycle. Similarly, lthetransmitting unit I2 is equipped with a fixed tuned amplitude modulationreceiver I9 which is tuned to a carrier frequency of 1700 kilocyclesandis" sharplyr selective to the 1699.700 and 1700.300

1n kilocycle waves respectively radiated by the transmitter 2| and thetransmitter of the unit w.'

Here again, the selectivity of the receiver I9 is obviously such thatthe carrier waves radiated by the transmitter 20 and the transmitter ofthe by the receiver I9 is reproduced in the audio fre- K quency sectionthereof and modulated upon-the 20 carrier wave voutput of thetransmitter embodied band pass filter 9 which is'center tuned to afrequency of 0.600 kilocycle.

Referring now particularly to the equipment I tus associated therewith,it will be noted that this.

equipment comprises a pair of iixed tuned amplitude modulation receivers26 and 21, the output :so circuits of which .are respectively connecteda through suitable amplifier and automatic gain or Vvolume controlstages '32 and 33 to a pair ofphase.

comparison devices or phase meters 30 and 3| and a pair of narrow bandpass filters 28 and 29 3,-, center tuned to frequencies of 0.600 and0.250 kilocycles. More specifically, the receiver26 is fixed tuned to acarrier frequency of 1700 kilocycles and is designed to accept thecarrier wave radiated by the transmitter 2| and the carrier .40 waveradiated lby the transmitterof the unit I0 both when modulated andunmodulated. Similarly, the receiver 27 is fixed tuned to a carrierfrequency of 1602 kilocycles and is designed to acceptthe carrier waveradiated by the transmitter 20 and the carrier wave radiated by thetransmitter of the unit I2 `both when modulated andv unmodulated.

'I'he automatic gain control or AVC circuits associated with theV,amplifier stages 32 and 33 are f of the variable impedance type knowninthe art and capable, of yfunctioning without introducingamplitudedistortion ory variable phase shift in the reference signalsand the heterodyne or differencevw frequency signals developed at theoutput terminalsmf .1 the receivers. Preferably the amplifierand AVC'stages are of the type disclosedin a copending,application of James E.Hawkins; and-.lesseRJCornett Serial No. 673,744 filed June .1, :1.946,'Patent No. 2,554,905 granted May 29,195 1,jforfSeilsmic SignalAmplifier and assigned to the sameV assignee as the present inventionandjeachofthe'se stages corresponds to the automatic gain control andamplifier stage identiiied by the reference number I3 in the saidHawkins and Cornett application.

'I-he filters l' 28 and 29, which may be of any standard commercialconstruction, perform the function of selecting the heterodyne ordifference frequency signals alternately developed at the outputterminals of the receivers 26 and 27, respectively, and amplified in thestages 32 and 33 and delivering these signals to the phase meters 3| and30. respectively.

As indicated in the above mentioned copending application Serial No.42,648, the phase Ain the transmitting unit I2 througha narrow meters 20and 2| may be of the general character disclosed in Morrison Patent No.1,762,725.,

granted June 10, 1930, which are capable of measuring phase angles inexcess of 360 electrical degrees between two impressed signal voltagesand which include rotatable rotors or indicator members 2l and 35respectively. PreferabLv, however, the phase meters 30 and 2| constitutenull type motor driven phase indicating apparatusgof the type describedand claimed in the abovel referred to copending application Serial No.100,382. As there described, the rotatable members carry a pointer whichindexes with a circular scale to indicate the phase relationship betweenthe two impressed voltages. In accordance with the present invention,however, the rotatable members 24 and 25 are employed as hereinafterdescribed to drive a computing and tracing mechanism so as to indicatecontinuously on a map or chart the position of the receiving unit I3.

Before describing in detail the construction and operation of thecomputing and tracing mechanism driven by the rotatable members 34 and35 of the phase meters 30 and 3|, the operation of the transmitting andreceiving apparatus of the position determining system will be morefully explained.

It will be understood that when the motor and gear train unit 23 isoperating to drive the commutating ring 22, anode current is alternatelydelivered to the electron discharge tubes of the transmitters 20 and 2|,such that these transmitters are alternately rendered operative toradiate carrier waves at frequencies of 1601.875 and 1699.700kilocycles, respectively. The transmitters of the units I and I2, on theother hand, operate continuously. Accordingly, during each interval whenthe transmitter 20 is in operation, the carrier waves of 1601.875 and1602.125 kilocycles respectively radiated by the transmitter 20 and thetransmitter of the unit I2 are picked up and heterodyned in the' radiofrequency sections of the receivers I6 and 21. In the receiver I6, thedifference frequency signal of 0.250 kilocycle is reproduced in theaudio section of the receiver, passed by the filter 8 and modulated uponthe carrier wave output of the transmitter in the unit I0 for radiationas a reference signal. If desired an amplifier and automatic gaincontrol stage similar to the stages 32 and 33 may be interposed in theoutput circuit of the receiver I6 in order to maintain constantmodulation. 'Ihis modulated carrier wave is received by the receiver 26of the mobile receiving unit I3 and the 0.250 kilocycle modulationcomponent is reproduced at the output terminals of this receiver. Duringthe period indicated, the transmitter 2| is not in operation and henceno heterodyne or beat frequency signal is developed by the receiver 25.,The 0.250 kilocycle reference signal as thus reproduced by the receiver26 is amplified to the proper level in the amplifier and AVC stage 32and applied to the right set of terminals of the phase meter 30 and alsoto the input terminals of the 0.600 kilocycles band pass lter 2B. Thisfilter rejects the applied signal and thus prevents the same from beingapplied to the right set of input terminals of the phase meter 3|.

The 0.250 kilocycle beat frequency or heterodyne signal resulting fromheterodyning of the carriers radiated by the transmitter 20 and thetransmitter of quency section of the receiver 21 is reprodiscriminatingand positions II and I2 the unit I2 in the radio freduced across theoutput terminals of this receiver and after amplification to the properlevel in the amplifier and AVC stage 22 is applied to the left set ofinput termi als of the phase meter 3| and the input terminals of the0.250 kilocycle band pass filter 29 in parallel. Since the filter 22prevents a signal from being applied to the right set of input terminalsof the phase meter 3|-, this phase meter does not respond to the signalvoltage applied to its left set of input terminals by the receiver 21.The filter 29. however, passes the 0.250 kilocycle signal developedacross the output terminals of the receiver 21 and applies the same tothe left set of terminals` of the phase meter II. Thus two signalvoltages of identical frequency are applied to the two sets of inputterminals of the phase meter Il, with the result that this phase meterfunctions to rotate its indicator element 24 to a position which isaccurately representative of the position of the receiving unit I2between two iso-phase lines of the standing waves producted in space asa result of the carrier wave radiation by the transmitter and thetransmitter of the unit I2. In Fig. 5, wherein the relative positions ofthe units I I and I2 are diagrammatically illustrated, the family ofhyperbolas shown in full lines and having the as focal points, arerepresentative of the isophase lines related to the transmission ofwaves from the transmitter 20 of the unit and the transmitter of theunit I2.

At the end of the described transmitting interval, the commutating ring22 functions to interrupt the circuit for delivering anode current tothe tubes of the transmitter 20, with the result that carrier waveradiation from this transmitter is terminated. When radiation of thiswave stops, the carrier heterodyning action of the two receivers I6 and21 is likewise terminated to interrupt the reference signal radiation bythe transmitter of the unit I0 and to interrupt the heterodyne ordifference frequency signal being developed across the output terminalsof the receiver 21. Thus the phase meter 30 is rendered ineffectivefurther to change the setting of the rotatable member 34.

A short time interval after operation oi' the transmitter 20 is stopped,the commutating ring 22 functions to deliver anode current to the tubesof the transmitter 2| and thus initiate operation of this transmitter.With the transmitter 2| in operation, a 1699.100 kilocycle positionindicating carrier wave is radiated thereby which is accepted by thereceivers I! and 26. More specifically, the receiver I9 functions toheterodyne the carrier wave radiated by the transmitter 2| with thecarrier wave radiated by the transmitter of the unit I0 and to reproducethe heterodyne or difference frequency signal of 0.600 kilocycle in theaudio frequency section thereof. This difference frequency or referencesignal is passed by the filter 9. modulated upon the output carrier waveof the generator I1 in the modulator and power ampliiler unit I8 andradiated as a modulation component upon the carrier wave transmitted bythe transmitter of the unit I2 to the receiver 21. As previouslymentioned in connection with the receiver I6 of unit I0, a suitableamplifier and automatic gain control stage may be interposed in theoutput circuit of the receiver I9 in order to maintain constantmodulation. The receiver 21 accepts the modulated carrier wave andreproduces the modulation component thereof in the usual manner. Thereference signal thus devel- 20 of the unit II' oped across the outputterminals of the receiver 2l is amplified to the proper level in theamplifier and AVC stage 33 and applied across the left set of inputterminals of the phase meter 3| and the input terminals of the bandvpass filter 29 in parallel. This filter functions to reject the appliedreference signal voltage and thus prevents the same from being impressedupon the left set of terminals of the phase meter 30. It will beunderstood that the receiver 21 is incapable of accepting the carrierwave radiated by the transmitter of the unit I0. Hence this receiver isprevented from heterodyning the carrier wave radiated by the transmitterof the unit I with the carrier wave radiated by the transmitter of theunit I2.

The 1699.700. and 1700.300 kilocycle waves respectively radiated by thetransmitter 2| and the transmitter of the unit I0 are both accepted bythe receiver 26 and heterodyned in the radio frequency section thereofto produce a heterodyne or difference frequency signal which is producedacross the output terminals of the receiver and after amplification tothe proper level in the amplifier and AVC stage 32 is applied to theright set vof input terminals of the phase meter 30 and the inputterminals of the filter 28 in parallel. Since the i'llter 29 prevents asignal from being applied to the left set of input terminals of thephasel meter 30, this phase meter does not respond to the signal voltageapplied to its right set oi? terminals by the receiver Z. The 0.600kilocycle reference signa] applied to input terminals of the filter 28is passed by this filter and applied to the right set of input terminalsof the phase meter 3|. Thus reference and heterodyne or differencefrequency signals of identical frequencies are respectively applied tothe two sets of input terminals of the phase meter 3| which functions tomeasure the phase relationship between the two applied signal voltagesand rotate its indicator element 35 to a position accuratelyrepresentative of the position of the receiving unit I3 between twoiso-phase lines of the standing waves produced in space by the radiationof position indicating carrier waves from the transmitter 2l of the uniti l and the transmitter at the unit l0. These iso-phase lines arerepresented in Fig. 5 by the family of hyperbolic curves shown in brokenlinesand having as focal points the positions ii and i0.

At the end of the described transmitting interval, the commutating ring22 functions to interrupt anode current iiow to the tubes of the'transmitter 2i and thus arrest operation of this transmitter. Whencarrier wave radiation by the transmitter 2i is thus terminated, thewave heterodyning action eected in the receivers I9 and 26 is instantlystopped to terminate the radiation of 0.600 kilocycle reference signalby the transmitter of the unit i2 and to terminate reproduction of thedii rence or heterodyne signal at the output termin s of the receiver26. Thus the application of signal voltages to the two sets ci inputterminals of the phase meter Si is interrupted, with the result that nofurther change in the setting of the indicating element 35 can beproduced. A short time interval after operation of the transmitter 2i isarrested, the commutating ring22 functions to recomplet'e thecircuit fordelivering anode current to the tubes of the transmitter 20 and thusreinitiate operation of this transmitter with the results-describedabove.-

Fromthe foregoing explanation, it 'will be' understood that thetransmitters 20 'and 2l in their alternate operation to radiate positionindicating carrier waves cooperate with the receivers I6 and I9 of thetransmitting units I0 and I2 alternately to render the transmitters ofthese units operative to radiate position indicating signals andreference signals. More in particular, the position indicating carrierwaves alternately radiated by the transmitters 20 and 2| alternatelycause the position indicating carrier waves respectively radiated by thetransmitters of the units l0 and I2 to be modulated with referencesignals during periods when these transmitters are respectively inactiveas position indicating signal radiators. Specifically, the receiver 26functions as a heterodyne receiver in respect to the position indicatingcarrier waves radiated by the transmitter 2l and the transmitter of theunit I0, and functions as a reference signal reproducing receiver inreceiving the reference signal modulated carrier radiated by thetransmitter of the unit I0. The receiver 2l, on the other hand,functions as a heterodyne receiver in respect to the position indicatingcarrier waves radiated by the transmitter 20 and the transmitter of theunit I2 and as a reference signal detecting receiver in receiving thereference signal modulated carrier wave radiated by the transmitter ofthe unit I2.

As previously indicated, the alternate rotary movements of the rotatablemembers 3B and 35 of the phase meters 30 and 3l respectively constitutemeasures of the position of the mobile receiving unit I3 relative to twosets of iso-phase lines having focal points at the positions I2, I I andI0, the position Ii being common to the two sets. In accordance with thepresent invention the rotatable members 3d and 35 are arranged tooperate a computing and tracing mechanism 37 which, as shown in Figs. 1to 4, inclusive, comprises a tracing member 38, the position of which isrepresentative of the receiving unit I3 and which forms a common pivotfor a plurality of extensible and retractable arm members 39, i0 and diwhich are respectively connected for longitudinal adjustment to suitablemotion transmitting means t2, e3 and Mi, the respective positions ofwhich correspond to the locations of the transmitting units i0, il andi2. rIhe tracing member 3B may be of any desired construction but isshown in Fig. i as comprising a pivot pin which extends through and isrotatably mounted in a plurality of extending ears 39a, #30a and Marespectively carried by the arms 39, 10 and iii. It will, of course, beunderstood that if a permanent record of the movements of the tracingmember 38 is desired, or if the mechanism is to be used to plot anintersection grid chart, the tracing member 38 may take the form of amarking member such as stylus or other suitable record producing member.The arm members and the associated motion transmitting means maylikewise be of any suitable construction in which operation of themotion transmitting means is effective to adjust the length of the arms,and in the embodiment shown, the arms 39, 30 and l have been illustratedas rack members having suitable rack teeth thereon adapted to mesh withrack gears e5, i6 and @i forming part of the motion transmitting means.

\ The respective center lines of the rack gears 515,

35 and tl constitute the focal points corresponding to the positions ofthe transmitter units i3, ii and I2, and it will be noted that the arms39, @0 and 6i are odset from the center lines a distance equal to theradius of the rack gears. The displacement error thus introduced.however, is compensated for by the ears 38a, 48a and 4|a, which extendfrom the arms an equa-l distance and carry the tracing member 38.

Respectively disposed between the motion transmitting means 43 and 44and between the motionv transmitting means 42 and 43 are a pair ofdifferential mechanisms 48 and 49 which are respectively arranged tol bedriven by the rotatable members 34 and 35 of the phase meters 38 and 3|.Thus the rotatable member 35 is shaft connected as indicated by thebroken line 58 to the rotor of a servo-generator trically connected asindicated by the conductors 52 to a servo-motor 53 which drives a shaft54 carrying a worm 55 adapted to mesh with a worm gear 56 on the drivingshaft 51 of the differential mechanism 49. The servo system comprisingthe servo-generator 5| and the servomotor 53 may be of any well knowntype available in the art and it will, of course, be understood that ifthe phase capable of developing sufllcient torque to drive thedifferential 49 and the mechanism connected thereto, the servo systemmay be eliminated and the shaft of the phase meter may be connecteddirectly to the differential through the worm 55 and the worm gear 56which provide a unidirectional or irreversible driving connection.

Mounted on the shaft 51 of the differential is a spider 58 which carriesa pair of spider pinions 59 and 68 arranged to mesh with a pair ofoppositely disposed differential pinions 6| and 62 which are rotatablymounted on the shaft 51 and carry suitable spur gears 63 and 64'whichrespectively mesh with cooperating spur gears 65 which is elec-` meter3| is of a type and 66 secured to shafts 61 and 68 which extend to therespective motion transmitting means 42 and 43 and are provided withbevel gears 69 and 18 which are arranged to mesh with additional bevelgears 1| and 12 which form parts of the motion transmitting means andare respectively carried by the rack gears and 46.

Similarly the phase meter 38 is shaft connected as indicated by thebroken line 13 to a servogenerator 14 which is electrically connected toa servo-motor 15, the shaft of which carries a worm 16 meshing with aworm gear 11 on the driving shaft 16 of the differential mechanism 48.The differential mechanism 48, which is identical with the differentialmechanism 49, vincludes a spider 19, a pair of spider mounted pinions 68and 8|, oppositely disposed differential pinions 82 and 83, and a pairof spur gears 84 and 85 arranged to mesh with the spur gears 86 and 81which are respectively mounted on the drive shaft 88 and 89 extending tothe motion transmitting means 43 and 44. Asshown, the shaft 88 carriesa. bevel gear 98 which forms a part of the motion transmitting means 43and is arranged to mesh with the bevel gear 12 in reverse relationrelative to the bevel gear 18. Likewise the shaft 89 carries at itsouter end a bevel gear 8| which forms a part of the motion transmittingmeans 44 and is arranged to mesh with a cooperating bevel gear 92carried by the rack gear 41.

In order to carry out a position tracing operation it is, of course,necessary that the starting point ofA the mobile receiving unit I3 andconsequently of the tracing member 38 be known. For purposes ofdescription it will be assumed that the unit I3 is at the positionrepresented by the letter A in Fig. 5 and that during the interval to bedescribed it moves to the position B; During the first portion of themovement of the receiving unit it will be assumed that the transmitterat the unit I8 and the transmitter 2| at the unit are operating asheretofore described to cause rotary movement of the measuring orindicating member 36 of the phase meter 3| in a direction such as torotate the drive shaft 61 of the differential mechanism 48 in thedirection indicated by the arrow in Fig. l immediately adjacent theshaft 51. Throughout the drawings the arrows shown adjacent the variousrotating shafts and gears indicate the direction of movement of the topof the said shafts and Sears.

The consequent rotation of the spider 58 carrying the spider pinions 69and 68 will effect rotation of thediiferential pinions 6| and 62 and thespur gears 63 and 64 in the direction indicated by the arrows, which,through the gears 66 and 66, will drivethe shafts 61 and 83 irnthe samedirection as again indicated by arrows. It will be observed that therack gear 45 of the motion transmitting means 42 engages the rack teethon the inner side of the arm 39, while rack gear 46 at the motiontransmitting means 43 engages the rack teethA on the outer side of thearm 48 and consequently the arms 38cand 48 will be driven in' oppositedirections again as indicated by arrows. the arm 38 tending to shortenand the arm 48 tending to lengthen. The effect of such adjustment of thearms 39 and 48 tends to move the tracing member 38 from the point A in adirection indicated by the arrow |88 in Fig. 5, and the amount ofmovement is proportional to the amount of rotation of the rotatablemember 35 of the phase meter 3|, one complete rotation, i.e., 360degrees, thereof being effective to move the tracing element from one ofthe isophase lines shown in broken lines in Fig. 5 to the next adjacentiso-phase line of the same family. If the tracing and computingmechanism included only the arms 39 and 48 and the diier- 1 entialmechanism 49, that is if the arm 4| and its connection through thedifferential 46 to the motion transmitting means 43 were omitted, the,ltracing point 88 when driven through the differ` ential 49 from thephase meter 3| would trace an elliptical path having the points I8 andIl as foci, which elliptical path would intersect the hyperbolas shownin broken lines in Fig. 5 atl However, the arm 4|, as hereinafterdescribed, is effective to convert this elliptical path to a hyperbolicpath having foci at the right angles.

points and I2, this conversion being permitted by differential action ofthe differential 48.

Since the motion transmitting means 43 which is being driven by thedifferential 49 is connected through the bevel gear 98 to the shaft 68,the bevel gears 18 and 98 being in reverse relation, the shaft 88 willbe driven in the direction indicated by the arrow in Fig. 1, and sincethev spider 19 and the shaft 18 of the differential 43 are heid againstreverse rotation by reason of the irreversible connection provided bythe worm 16 and the worm gear 11, rotation of the differential pinion 82through the gears 66 and 84 will effect rotation of the spider mountedpinions 88 and 8| so as to drive the spur gears 85 and 81 andconsequently the shaft 89 in the direction indicated by the arrow, withthe result that the arm 4| will be driven by the motion transmittingmeans 44 in a direction tending to lengthen the arm 4|. Thus it will beobserved that the arms 48 vand 4I, which are positively connectedtogether through the `differential 4 8, are simultaneously lengthened,and since the various gearing arrangements have equal ratios, the arms48 Fig. l,

are connected by means of an irreversible connection (not shown) and apair of shafts I I5 and ||6 to bevel gears I|1 and I|8 whichrespectively constitute portions of differential mechanisms |I9 and |20.Also included in the differential mechanisms 'II9 and |20 are opposedpairs of bevel gears |2I, |22 and |23, |24, respectively arranged todrive a plurality of shafts |25, |26, |21 and |28.

The shafts |21 and |28 which are driven by the differential respectivelyterminate in .motion transmitting means |29 and |30 which are similar tothe, motion transmitting means 42, for example, of Fig. l, and whichdrivingly engage suitabley rack teeth on a pair of extensible andretractable arms |3| and |32. Similarly the shafts |25 and |26 which aredriven by the differential mechanism II9 are respectively conf nected tomotion transmitting means |33 and |34, which drivingly engage extensibleand retractable arm members and |36. The motion transmitting means |29,|30, |33 and |34 are respectively located in positions corresponding tothe focal points of a hyperbolic intersection grid, the motiontransmitting means |29 and |34, which may, if desired, be superimposedon a single vertical axis, constituting the common focal point. Sincethe motion transmitting means |29 and |34 represent focal points of twoseparate sets of hyperbolas, it is not necessary that they besuperimposed and it may be advantageous in special instances to employ,in radio position finding systems embodying the invention, a transmitterarrangement for producing two sets of hyperbolas with the central focalpoints separated a considerable distance. All of the arms |3|, |32, |35and-|36 are pivotally connected at a common pivot point to a tracingmember |31 which, as shown in Fig. 7, comprises a pivot pin |38 whichrotatably carries a pair of gears |39 and |40, the arms |3| and |32being adapted to mesh with the gear |39 and the arms |35 and |36 beingarranged to mesh with the gear |40. It will be understood that suitablefollower or guide means (not shown) are employed for maintaining all ofthe arms in meshing relation with the gears |39 and |40 and that similarmeans are employed at the various motion transmitting `means both inthis embodiment of the invention-and in the previously describedembodiment. With the above described arrangement it will be apparentthat when the driving device ||3, for example, is operated to rotate thedifferential gears ||1, |2| and |22 so as to rotate the shaftsv |25 and|26 in the direction indicated by the small arrows. the motiontransmitting means |33 and |34 respectively driven thereby will adjustthe arms |35 and |36 so as effectively to lengthen the arm |35 whilecorrespondingly shortening the arm |36. The consequent movement of thetracing member |31 will be generally downward and to the right from theposition shown in Fig. 6, and since the arms |3| and |32 mesh with thesame gear |39 on the pivot pin |30, relative movement of these arms isprevented and they will accordingly be adjusted so as simultaneously toshorten both the arms |3I and |32, thereby causing the tracing member|31 to move along the hyperbolic path represented by the line |40. Thesimultaneous shortening of the arms I3I and |32 is effective through themotion transmitting means |29 and |30 to drive the shafts |21 and |28 inthe same direction, as indicated by the arrows, which, through thedifferential mechanism |20 cause the entire driving device 4, togetherwith the shaft I|6 and the gear II8 t0 rotate about the axis of theshafts |21 and |28, which is permitted due to the fact that the drivingdevice ||4 is mounted on a suitable slip ring structure |4| for bodilyrotation about the shaft |28, the slipring structure |4| being providedto effect the electrical connections to the driving device I I4 whilepermitting the above described bodily movement thereof.

The line |40 along which the tracing member moves during the abovedescribed operation constitutes a hyperbolic path having its focalpoints at the positions occupied by the motion transmitting mechanism|30 and the motion transmitting mechanism |29. Upon operation of thedriving device ||4, the arms and the tracing point will be moved in asimilar manner to cause the tracing member |31 to move along ahyperbolic path having as its focal points the locations of the motiontransmitting means |33 and the motion transmitting means |34, thedriving device |I3 likewise being mounted on a slip ring structure |42for rotation about the shaft |26 during the intervals that the drivingdevice ||4 is in operation.

. The embodiment of the invention shown in Fig. 8 is in all respectssimilar to the embodiment of Fig. 1 except that the arm 40 of Fig. l hasbeen omitted and corresponding parts are identified by the samereference numerals. Since the motion transmitting means 43 interconnectsthe shafts 68 and 88, it will be apparent that operation of either oneof the servo-motors 53 or 15 will cause movement of both of the arms 39and 4I so as to adjust the tracing member 38 exactly as in theembodiment of Fig. l so long as the tracing member 38 is operatingwithin the area bounded by the lines |43 and |44. In this arealengthening of one of the arms will be accompanied by simultaneousshortening of the other arm in tracing hyperbolic paths, but omission ofthe arm 40 renders the computing and tracing apparatus incapable ofreversing the sign of the movement of one of the arms as is requiredwhen tracing hyperbolic paths outside of this particular area aspreviously described in connection with the embodiment of Fig. 1.

While particular embodiments of the invention have been shown, it willbe understood, of course, that the invention is not limited theretosince many modifications may be made and it is therefore contemplated bythe appended claims to cover any such modications as fall within thetrue spirit and scope of the invention.

What is claimed as new and desired to be secured by Letters Patent ofthe United States is:

1. In a radio position finding system of the hyperbolic continuous wavetype employing phase comparison in pairs of position indicating signalsradiated from at least three spaced transmitting points to provide apair of indications from which the position of a mobile receiving pointrelative to the known positions of the transmitting points may bedetermined, the combination of receiving apparatus at said mobile pointincluding phase measuring means having a pair of indicator membersrotatable to provide said indications, means including a chart providingrepresentations of the known positions of said transmitting pointsrelative to the area represented by said chart, and mechanical computingapparatus including a plurality of differential mechanisms havingspiders driven by said indicator members and means adjustable on saidchart with respect to said known positions and driven by said differ- 17ential mechanisms in tation of said indicator members to indicatecontinuously on said chart the position of said receiving apparatus.

2. In a radio position finding system of the hyperbolic continuous wavetype employing phase comparson in pairs of position indicating signalsradiated from at least three spaced transmitting points to provide apair of indications from which the position of a mobile receiving pointrelative to the known positions of the transmitting points may bedetermined. the combination of receiving apparatus at said mobile pointincluding phase measuring means having a pair of indicator membersrotatable to provide said indications, means including a chart providingrepresentations of the known positions of said transmitting pointsrelative to the area represented by said chart and constituting thefocal points of a pair of intersecting families of hyperbolas, andmechanical s computing apparatus including means movable over said charthaving adjustable connections to at least two of said focal points andincluding a plurality of spider-driven differential mechanisms foradjusting said connections in accordance with the rotation of saidindicator members, whereby the movement of said movable means over saidchart continuously indicates the position of said receiving apparatus.

3. In a radio position finding system of the hyperbolic continuous wavetype employing phase comparison in pairs of position indicating signalsradiated from at least three spaced transmitting points to provide apair of indications from which the position of a mobile receiving pointrelative to the known positions of the transmitting points may bedetermined, the combination of receiving apparatus at said mobile pointincluding phase measuring means having a pair of indicator membersrotatable to provide said indications, and mechanical computingapparatus comprising a plurality of motion transmitting means located inspaced apart relation representative of said three spaced transmissionpoints, a movable member representative of the instantaneous positionsof said receiving apparatus relative to said transmission points, a pairof extensible and retractable means pivotally connected to said movablemember and respectively connected to the two most remotely spaced ofsaid motion transmitting means, a pair of differential mechanismsrespectively connected between the intermediate one of said motiontransmitting means and the said two remotely spaced motion transmittingmeans, and irreversible means for respectively connecting said rotatableindicator members in driving relation to said diierential mechanisms,whereby said movable member is moved to indicate continuously theposition of said receiving apparatus.

4. In a radio position finding system of the hyperbolic continuous wavetype employing phase comparison in pairs of position indicating signalsradiated from at least three spaced transmitting points to provide apair of indications from which the position of a mobile receiving pointrelative to the known positions of the transmitting points may bedetermined, the combination of receiving apparatus at said mobile pointincluding phase measuring means having a pair of indicator membersrotatable to provide said indications, and mechanical computingapparatus comprising a plurality of motion transmitting means located inspaced apart relation representative of said three spaced transmissionaccordance with the ropoints,` a movable member representative of theinstantaneous -positions oi/said receiving apparatus relative to saidtransmission points, a pair of extensible and retractable meanspivotally connected to said movable member and respectively connected tothe two most-remotely spaced of said motion transmitting means, a pairof differtial mechanisms each having. a pair of spidermounted pinionsand a pair of opposed diierential pinions meshing with saidspider-mounted pinions, irreversible means for respectively connectingsaid indicator members in driving relation to the spiders of saiddiierentials, means respectively connecting one of said differentialpinions of each of said differentials to said remotely spaced motiontransmitting means, and means including the intermediate one of saidmotion transmitting means interconnecting the other differential pinionsof said differential mechanisms whereby operation of either of saidindicator members is effective to adjust both of said extensible andretractable means to move .Y said movable member along hyperbolic pathsthe focal points of which depend upon which of said indicator members isbeing operated, thereby to indicate continuously the position of saidreceiving apparatus relative to said transmission points.

5. In a position determining system having a mobile receiving point, apair of spaced transmitters continuously operative to radiatedistinguishable position indicating signals, a transmitting unit spacedfrom each of said transmitters and including means for alternatelyradiating two other distinguishable position indicating signals,heterodyning receivers respectively associated with said transmittersand each jointly responsive to the position indicating signal radiatedby the other transmitter and to a different one of the signals radiatedby said transmitting unit for alternately modulating the signalsradiated by said transmitters with reference signals having frequenciesrespectively equaling the diiference frequencies of the heterodynedsignals, a pair of receivers at said receiving point each operative toreceive and reproduce a different one of said reference signals, saidlast-named receivers also being alternately operative to heterodyne theposition indicating signals which have a difference frequency equalingthe frequency of the reference signal being reproduced by the otherreceiver of said pair and to reproduce such difference frequency signal,whereby two pairs of signals of matching frequencies are alternatelydeveloped at said receiving point, phase measuring means at saidreceiving point for measuring the phase relationship between the signalsof each pair and including a pair of members alternately rotatable inaccordance with said phase relationship to provide two measures of theposition of said receiving point relative to different ones of saidtransmitters, and a mechanical computing apparatus actuated by saidalternately rotatable members and including a chart representative of anarea blanketed by said transmitters and also including an elementalternately driven over said chart along hyperbolic paths in accordancewith the alternate rotation of said members to indicate continuously onsaid chart the position of said receiving point.

6. In a position determining system, a receiving point, a pair of spacedtransmitters continuously operative to radiate distinguishable positionindicating signals, a transmitting unit spaced from each of saidtransmitters and including means for alternately radiating two otherdistinguishable position indicating signals, heterodyning receiversrespectively associated with said transmitters and eachjointly'responsive to the position indicating signal radiated by theother transmitter and to a' different one of the signals radiated bysaid transmitting unit for alternately modulating the signals radiatedby said transmitters with reference signals having frequenciesrespectively equaling the difference frequencies of the heterodynedsignals, a pair of receivers at said receiving point each operative toreceive and reproduce a different one of said reference signals, saidlast-named receivers also being alternately operative to heterodyne theposition indicating signals which have a Adinerence frequency equalingthe frequency of the reference signal being reproduced by the otherreceiver of said pair and to reproduce such difference frequency signal,whereby two pairs of signals of matching frequencies are alternately.developed at said receiving point, phase measuring means at saidreceiving point for measuring the phase relationship between the signalsof each pair and including a pair of members alternately rotatable inaccordance with said phase relationship to provide two measures of theposition of said receiving point relative to different ones of saidtransmitters, and a .mechanical computing apparatus actuated by saidalternately rotatable members and including a chart representative of anarea blanketed by said transmitters and means representative of theknown positions of said spaced transmitters relative to said chart,motion transmitting means at said known chart positions, an indicatingelement movable over said chart and operatively connected to said motiontransmitting means, differential mechanisms respectively driven by saidrotatable members and respectively connected to said motion transmittingmeans, and means interconnecting said differential mechanisms wherebysaid indicating element is alternately driven along hyperbolic pathshaving as a focal point one or the other of said known chart positions,thereby to indicate continuously on said chart said position of saidreceiving apparatus.

7. In a position determining system having a mobile receiving point, apair of spaced transmitters continuously operative to radiatedistinguishable position indicating signals, a transmitting unit spacedfrom each of said transmitters and including means for alternatelyradiating two other distinguishable position indicating signals,heterodyning receivers respectively associated with said transmittersand each jointly responsive to the position indicating signal radiatedby the other transmitter and to a different one of the signals radiatedby said transmitting unit for alternately modulating the signalsradiated by said transmitters with reference signals having frequenciesrespectively equaling the difference frequencies of the heterodynedsignals, a pair of receivers at said receiving point each operative toreceive and reproduce a different one of said reference signals, saidlast-named receivers also being alternately operative to heterodyne theposition indicating signals which have a difference frequency equalingthe frequency of the reference signal being reproduced by the otherreceiver of said pair and to reproduce such difference frequency signal,whereby two pairs of signals of matching frequencies are alternatelydeveloped at said receiving point, phase measuring means at said re- 20l. ceiving point for measuring the phase relationship betweenthe'sig'nals of each pair and including a pair of members alternatelyrotatable to provide two measures of the position of said receivingpoint relative to different ones of said transmitters, and a mechanicalcomputing apparatus including a chart representative of an areablanketed by said transmitters and means Arepresentative of the knownpositions of said spaced transmitters relative to said chart, motiontransmitting means at each of said known chart positions, a movabletracing member, a

pair of extensible and retractable means pivotal-' said differentialmechanisms whereby alternate operation of said rotatable members iseffective through said differentials to move said tracing member alonghyperbolic paths having focal points which correspond to the positionsof said transmitters thereby to indicate continuously on said chart theposition of said receiving apparatus.

8. Wave signal receiving and position tracing apparatus for translatingreceived space radiated waves from at least three spaced transmissionpoints and continuously tracing the position of the receiving apparatuson a hyperbolic grid having focal points corresponding to the positionsof said transmitting points, one of the focal points being common to thetwo families of hyperbola forming said grid, comprising wave signalreceiving means responsive to said received waves in pairs for producingtwo pairs of signals, the signals of each pair having a phaserelationship representative of the position of said receiving apparatusrelative to said transmission points, phase measuring means energizeableby said pairs of signals and including a pair of elements respectivelyrotatable to positions indicative of said phase relationships, motiontransmitting means at said focal points, a movable tracing member, apair of extensible and retractable means pivotally connected to saidtracing member and respectively connected to said motion transmittingmeans at the two focal points other than said common focal point,differential mechanisms respectively connected between said motiontransmitting means at said common focal point and said motiontransmitting means at said two other focal points, and irreversiblemeans for respectively driving said differential mechanisms from saidrotatable elements of said phase measuring means.

9. Wave signal receiving and position tracing apparatus for translatingreceived space radiated waves from at least three spaced transmissionpoints and continuously tracing the position of the receiving apparatuson a hyperbolic grid having focal points corresponding to the positionsof said transmitting points, one of the focal points being common to thetwo families of hyperbola forming said grid, comprising wave signalreceiving means responsive to said re- 2l ceived waves in pairs forproducing two pairs of signals, the signals of each pair having a phaserelationship representative. of the position of said receiving apparatusrelative to said transmission points, phase measuring means energizeableby said pairs of signals and including a pair of elements respectivelyrotatable to positions indicative of said phase relationships, motiontransmitting means at said focal points, a movable tracing member, apair of extensible and retractable means pivotally connected to saidtracing member and respectively connected to said motion transmittingmeans at the two focal points other than said common focal point, a pairof differential mechanisms each having a pair of spider-mounted pinionsand a pair of opposed differential pinions meshing with saidspider-mounted pinions, means including an irreversible connection forrespectively driving the spiders of said differential mechanisms fromsaid rotatable elements of said phase measuring means, meansrespectively connecting one of said differential pinions of each of saiddifferential mechanisms to said motion transmitting means at said twoother focal points, and means including said motion transmitting meansat said common focal point interconnecting the other differentialpinions of said differential mechanisms, whereby rotation of either ofsaid rotatable elements is effective to adjust said extensible andretractable means to move said tracing member along hyperbolic paths.

l0. Wave signal receiving apparatus for translating received spaceradiated waves into position indications, comprising a receiveroperating to receive a first pair of space radiated waves and toheterodyne said Waves to produce a rst heterodyne signal having afrequency related to the difference frequency between said waves, saidreceiver being alternately operative to receive and reproduce a firstreference signal having a frequency representative of the differencefrequency between a second pair of radiated waves and modulated upon oneof said first pair of radiated waves, a second receiver operative toreceive and heterodyne said second pair of radiated waves to produce asecond heterodyne signal having la frequency equaling the frequency ofsaid first reference signal, said second receiver being alternatelyoperative to receive and reproduce a second reference signal having afrequency representative of the difference frequency between said rstpair of waves and modulated upon one of said second pair of Waves, phasemeasuring means alternately excited by said signals in pairs andincluding a pair of members alternately rotatable in accordance with thephase relationship between said first heterodyne and second referencesignals and between said second heterodyne and first reference signalsto provide two measures of the position of said receiving apparatusrelative to two displaced sources of said waves, and a mechanicalcomputing apparatus including a chart representative of an areablanketed by said waves and also including an element alternately drivenalong hyperbolic paths in accordancewith the rotation of said members toindicate continuously on said chart said position of said receivingapparatus.

1l. Wave signal receiving apparatus for translating received spaceradiated waves into position indications, comprising a receiveroperating to receive a first pair of space radiated waves and toheterodyne said waves to produce a first heterodyne signal having afrequency related to the difference frequency between said waves, saidreceiver being alternately operative to receive and reproduce a firstreference signal having a frequency representative of the differencefrequency between a second pair of radiated waves and modulated upon oneof said rst pair of radiated waves, a second receiver operative toreceive and heterodyne said second pair of radiated waves to produce asecond heterodyne signal having a frequency equaling the frequency ofsaid first reference signal, said second receiver being alternatelyoperative to receive and'reproduce a second reference signal having afrequency representative of the difference frequency between said firstpair of waves and modulated upon one of said second pair of Waves, phasemeasuring means alternately excited by said signals in pairs andincluding a pair of members alternately rotatable in accordance with thephase relationship between said first heterodyne and second referencesignals and between said second heterodyne and first reference signalsto provide two measures of the position of said receiving apparatusrelative to two displaced sources of said waves, and a mechanicalcomputing apparatus including a chart representative of an areablanketed by said waves and also including means representative of theposition of said two displaced sources of said waves relative to saidchart area, motion transmitting means at said two positions, anindicating element movable over said chart and operatively connected tosaid motion transmitting means, differential mechanisms connected toeach of said motion transmitting means and driven by said rotatableinembers, and means including a reversing gear interconnecting saiddifferential mechanisms, whereby said indicating element is alternatelydriven along hyperbolic paths to indicate continuously on said chartsaid position of said receiving apparatus.

l2. Apparatus for tracing, on a hyperbolic grid formed by anintersecting pair of families of hyperbolas having a common focal point,the position of an object the movements of which relative to saidfamilies are reflected by the rotation of a pair of driving elements;comprising motion transmitting means positioned at said common focalpoint and at the second focal point of each of said families; a movabletracing member; a pair of extensible and retractable means pivotallyconnected to said tracing member and respectively connected to saidmotion transmitting means at said second focal points; differentialmechanisms respectively connected between said motion transmitting meansat said common focal point and said motion transmitting means at saidsecond focal points; and irreversible means for respectively drivingsaid differential mechanisms from said driving elements.

13. Apparatus for tracing, on a hyperbolic grid formed by anintersecting pair of families of hyperbolas having a common focal point,the position of an object the movements of which relative to saidfamilies are reflected by the rotation of a pair of driving elements;comprising motion transmitting means positioned on said grid at saidcommon focal point and at the second focal point of each of saidfamilies, a movable tracing member, a pair of extensible and retractablemeans pivotally connected to said tracing member and respectivelyconnected to said motion transmitting means at said second focal points,a pair of differential mechanisms each* having a pair of spider-mountedpinions and a @samer pair of opposed differential pinions meshing withsaid spider-mounted pinions, irreversible means for respectively drivingthe spiders of said differential mechanisms from said driving elements,means respectively connecting one of said differential pinions of eachof said differentials to said motion transmitting means at said secondfocal points, and means including said motion transmitting means at saidcommon focal pointl interconnecting the other differential pinionsv ofsaid differential mechanisms whereby operation of either of said drivingelements is effective to adjust both of said extensible and retractablemeans to move said tracing member along hyperbolic paths the focalpoints of which depend upon which of said driving elements is beingoperated.

14. Apparatus for plotting an intersecting pair of families ofhyperbolic curves having a common focal point and having the secondfocal points of said families in spaced relation to Veach other',comprising motion transmitting means at each of said focal points, amovable tracing member, a pair of extensible and retractable meanspivotally connected to said tracing member and respectively connected tosaid motion transmitting means at said second focal points, differentialmechanisms respectively connected between said motion transmitting meansat said common focal point and said motion transmitting means at saidsecond focal points, and irreversible means for independently drivingsaid differential mechanisms.

15. Apparatus for plotting an intersecting pair of families ofhyperbolic curves having a com mon focal point and having the secondfocal points of said families in spaced relation to each other,comprising motion transmitting means at.

each of said focal points, a movable tracing member, a pair ofextensible and retractable means pivotally connected to said tracingmember and respectively connected to said motion transmitting means atsaid second focal points, a pair of differential mechanisms each havinga pair of spider-mounted pinions and a pair of opposed differentialpinions meshing with said spider-mounted pinions, driving meansincluding an irreversible connection for driving the spiders of saiddifferentials, means respectively connecting one of said differentialpinions of each of said differentials to said motion transmitting meansat said second focal points, and means including said motiontransmitting means at said common focal point interconnecting the otherdifferential pinions of said differential mechanisms whereby operationof either of said driving means is effective to adjust both of saidextensible and retractable meansA to move said tracing member alonghyperbolic paths the vfocal points of which depend upon which of saiddriving means is being operated.

16. Apparatus for plotting anl intersecting pair of families ofhyperbolic curves having a common focal point and having the secondfocal points of said families in spaced relation to each other,comprising motion transmitting means 'at each of said focal points, amovable tracing member, extensible and retractable means pivotallyconnected to said tracing member and respectively connected to saidmotion transmitting means, differential mechanisms respectivelyconnected between said motion transmitting means at said common focalpoint and said motion transmitting means at said second focal points,and irreversible means for independently driving said differentialmechanisms, whereby operation I of one of said driving means iseffective to plot hyperbolic curves in one of said familiesand to adjustsaid tracing member from one curve to another in the other of saidfamilies and operation of the other of said driving means is effectiveto plot hyperbolic curves in said other family and to adjust saidtracing member between curves in said one family.

1'7. Apparatus for plotting an intersecting pair of families ofhyperbolic curves having a common focal point and having the secondfocal points of said families in spaced relation to each other,comprising motion transmitting means at each of said focal points, amovable tracing member, extensible and retractable means pivotallyconnected to said tracing member and respectively connected to saidmotion transmitting means, a pair of differential mechanisms each havinga pair of spider-mounted pinions and a pair of opposed differentialpinions meshing with said spider-mounted pinions, driving meansincluding an irreversible connection for driving the spiders of saiddifferentials, means respectively connecting one of said differentialpinions of each of said differentials to said motion transmitting meansat said second focal points, and means including said motiontransmitting means at said common focal point/interconnecting the otherdifferential pinions of said differential mechanisms whereby operationof either of said driving means is effective to adjust all of saidextensible and retractable means to move said tracing memting means atsaid focal points; differential.

ber along hyperbolic paths the focal points of which depend upon whichof said driving means is being operated.`

18. Apparatus for tracing, on a hyperbOlic grid formed by anintersecting pair of families of hyperbolas having a common focal point,the position of an object the movements of which relative to saidfamilies are reflected by the rotation of a pair of driving elements;comprisingv motion transmitting means positioned at said common focalpoint and at the second focal point of each of said families; a movabletracing member; extensible'and retractable means pivotally connected tosaid ltracing member and respectively connected to said motiontransmitmechanisms respectively connected between said motiontransmitting means at said common focal point and said motiontransmitting means at said second focal points; land irreversible meansfor respectively driving said diiferential mechanisms from said drivingelements.

19. Apparatus for tracing, on a hyperbolic grid formed by anintersecting pair of families of hyperbolas having a common focal point,the position of an object the movements'of which relative to saidfamilies are reflected by the rotation of a pair of driving elements;comprising motion transmitting means positioned on said grid at saidcommon focal point and at the second focal point of each of saidfamilies, a movable tracing member, extensible and retractable meanspivotally connected to said tracing member and respectively connected tosaid motion -transmitting means at said focal points, a pair ofdifferential mechanisms each having a pair of spider-mounted pinions anda pair of opposed rdifferential pinions meshing with said spidermountedpinions, irreversible means for respec- -tively driving the spiders ofsaid differential mechanisms from said driving elements, meansrespectively connecting one of said differential pinions of each of saiddifferentials to said motion transmitting means at said second focalpoints,` and means including said motion transmitting means at saidcommon focal point interconnecting the other differential pinions ofsaid differential mechanisms whereby operation of either of said drivingelements is effective to adjust all of said extensible and retractablemeans to move said tracing member along hyperbolic paths the focalpoints of which depend upon which of said driving elements is beingoperated.

20. Apparatus for plotting an intersecting pair A of families ofhyperbolic curves having a common focal point and having the secondfocal points of said families in spaced relation to each other,comprising motion transmitting means at each of said focal points, amovable tracing member, extensible and retractable means pivotallyconnected to saisi tracing member and respectively connected to saidmotion transmitting means at said focal points, differential mechanismsrespectively connected between said motion transmitting means at saidcommon focal point and said motion transmitting means at said secondfocal points, and irreversible means for independently driving saiddiierential mechanisms.

21. Apparatus for plotting an intersecting pair of families ofhyperbolic curves having a common focal point and having the secondfocal points of said families in spaced relation to each other,comprising motion transmitting means at each of said focal points, amovable tracing ,memben three extensible and retractable means pivotallyconnected to said tracing member and respectively connected to saidmotion transmitting means at said focal points, a pair of differentialmechanisms each having a pair of spidermounted pinions and a pair ofopposed differential pinions meshing with said spider-mounted pinions,driving means including an irreversible connection for driving thespiders of said differentials, means respectively connecting one of saiddifferential pinions of each of said differentials to said motiontransmitting means at said second focal points, and means including saidmotion transmitting means at said common focal point interconnecting theother differential pinions of said differential mechanisms wherebyoperation of either of said driving means is effective to adjust all ofsaid extensible and retractable means to move said tracing member alonghyperbolic paths the focal points of which depend upon which of saiddriving means is being operated.

22. In a radio position finding system of the hyperbolic continuous wavetype employing phase comparision in pairs of position indicating signalsradiated from at least three spaced transmitting points to provide apair of indications from which the position of a mobile receiving pointrelative to the known positions of the transmitting points may bedetermined, the combination of receiving apparatus at said mobile pointincluding phase measuring means having a pair of indicator membersrotatable to provide said indications, a plurality of differentialmechanisms having spiders driven by said indicator members, andmechanical computing apparatus including cooperating relatively movablechart means and position indicating means, said chart means providingrepresentations of the known positions of said transmitting pointsrelative to the area represented by said chart, and means driven by saiddifferential mechanisms in accordance with the rotation of saidindicator members for causing relative movement between said chart meansand said indicating means to indicate continuously on said chart theposition of said receiving apparatus.

23. In a position determining system having a mobile receiving point, apair of spaced transmitters continuously operative to radiatedistinguishable position indicating signals, a transmitting unit spacedfrom each of said transmitters and .including means for alternatelyradiating two other l distinguishable position indicating signals,heterodyning receivers respectively associated with said transmittersand each jointly responsive to the position indicating signal radiatedby the other transmitter and to a different one of the signals radiatedby said transmitting unit for alternately modulating the signalsradiated by said transmitters with reference signals having frequenciesrespectively equaling the difference frequencies of the heterodynedsignals, a pair of receivers at said receiving point each operative toreceive and reproduce a different one of said reference signals, saidlast-named receivers also being alternately operative to heterodyne theposition indicating signals which have a diil'erence frequency equalingthe frequency of the reference signal being reproduced by the otherreceiver of said pair and to reproduce such difference frequency signal,whereby two pairs of signals of matching frequencies are alternatelydeveloped at said receiving point, phase measuring means at saidreceiving point for measuring the phase relationship between the signalsof each pair and including a pair of members alternately rotatable inaccordance with said phase relationship to provide two measures of theposition of said receiving point relative to different ones of saidtransmitters, a mechanical computing apparatus actuated by saidalternately rotatable members and including cooperating relativelymovable chart means and indicating means, said chart means beingrepresentative of an area blanketed by said transmitters, and means forcausing relative movement between said chart means and said indicatingmeans whereby said indicating means effectively moves along hyperbolicpaths over said chart in accordance with the alternate rotation of saidmembers to indicate continuously on said chart the position of saidreceiving point.

24. Wave signal receiving apparatus for translating received spaceradiated waves into position indications, comprising a receiveroperating to receive a first pair of space radiated waves and toheterodyne said waves to produce a iirst heterodyne signal having afrequency related to the difference frequency between said waves, saidreceiver being alternately operative to receive and reproduce a rstreference signal having a frequency representative of the differencefrequency between a second pair of radiated Waves and modulated upon oneof said rst pair of radiated Waves, a second receiver operative toreceive and heterodyne said second pair of radiated Waves to produce asecond heterodyne signal having a frequency equaling the frequency ofsaid first reference signal, said second receiver being alternatelyoperative to receive and reproduce a second reference signal having a,frequency representative of the difference frequency between said firstpair of waves and modulated upon one of said second pair of waves, phasemeasuring means alternately excited by said signais in pairs andincluding a pair of members a1- ternately rotatable in accordance withthe phase relationship between said first heterodyne and secondreference signals and between said second heterodyne and first referencesignals to provide two measures oi the position or said receivingapparatus relative to two displaced sources of said waves, a mechanicalcomputing apparatus including cooperating relatively movable chart meansand indicating means, said chart means being representative of an areablanketed by said waves, and means for causing relative movement betweensaid chart means and said indicating means whereby said indicating meanseiectively moves along hyperbolic paths over said chart in accordancewith the alter nate rotation o! said members to indicate continuously onsaid chart the position of said receiving apparatus.

JAMES E. Hawms. ROBERT w. BAL'rossEa.

REFERENCES CITED The following references are of record in the o le ofthis patent:

UNITED STATES PATENTS Number

